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A  SHORT  STORY  OF 

CHARLES  BABBAGE 


AND  HIS 


CALCULATING  MACHINES 


Part  One 


January,  1905 


WYMAN  &  GORDON 

CLEVELAND.  OHIO 
WORCESTER.  MASS 


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A  Short  Story  of 

Charles  Barrage 

AXD  HIS 

CABCT  LATINO  MACHINES 

-  PJiRT  ONE  - 


.Jani:arv  IDO." 

M'VMAN  cSi  CiORDON 

(’LKVEi.ANi),  OHIO  >voRC ’i<:sti-:h,  mass. 


CHARLES  BABBAGE 


HIS  Short  Story  will  be  divided  into  Two  Parts,  on 
account  of  the  space  necessary  to  describe,  even 
in  the  briefest  manner,  the  inventions  of  this  most 
remarkable  man.  Very  little  is  known  about  his  home 
life,  although  he  lived  very  recently;  the  invention  so  far 
transcended  the  man  in  importance,  that  the  details  of 
his  life  seem  to  have  dropped  out  of  sight. 

Charles  Babbage  was  born  on  the  26th  of  Decem¬ 
ber,  1791,  at  Totnes,  Devonshire,  England.  His 
parents  were  wealthy  and  sent  him  to  a  private  school 
to  be  educated. 

He  entered  Trinity  College,  Cambridge,  in  1810. 
He  early  showed  a  marked  interest  in  mathematics,  and 
it  is  recorded  that  he  was  familiar  with  the  works 
of  the  great  mathematicians  before  he  went  to  college. 
He  graduated  from  Trinity  in  1814  with  high  rank 
in  mathematics,  then  traveled  and  continued  his  studies 
privately.  His  first  published  essay  was  on  the  Calculus 
of  Functions,  in  the  Philosophical  Transactions  of  1815. 
He  was  made  a  fellow  of  the  Royal  Society  in  1816, 
and  labored  with  Herschel  and  Peacock  to  raise  the 
standard  of  mathematical  instruction  in  England. 

He  early  noticed  the  number  and  importance  of 
errors  in  astronomy  and  other  calculations  due  to  errors 
in  mathematical  tables.  (The  first  idea  of  a  calculating 
machine  came  to  him  in  1812  or  1813,  while  still  a 
student/  Some  years  later  he  went  to  Paris  to  study 


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their  methods  for  computing  and  printing  the  now  cele¬ 
brated  French  tables  of  powers,  roots,  circumferences, 
areas,  sines,  tangents,  logarithms,  etc.  There  he  met 
several  of  the  most  noted  mathematicians  of  the  day. 
He  bought  a  copy,  at  a  high  price,  of  Didot’s  natural 
sines,  carried  to  the  twentieth  place  in  figures.  By  the 
permission  of  the  French  officials,  he  copied  by  hand 
to  the  fourteenth  place,  from  the  tables  of  logarithms 
deposited  in  the  Observatory,  every  500th  number  from 
10,000  to  100,000. 

All  scientific  callings  require  these  tables,  but  espe¬ 
cially  astronomers  and  navigators.  These  tables  are  now 
seen  in  every  engineer’s  hand-book,  and  we  little  appre¬ 
ciate  the  labor  and  expense  involved  in  their  preparation. 
It  is  of  interest  to  consider  the  extreme  care  that  was 
taken  to  prepare  them.  The  work  of  calculating  these 
tables  was  entrusted  at  Paris  to  three  corps  of  calcula¬ 
tors,  the  first  section  investigated  the  various  formulae 
and  selected  the  ones  that  could  most  readily  be  adapted 
to  simple  numerical  calculation  by  many  individuals. 
The  second  section  consisted  of  seven  or  eight  trained 
students,  who  converted  the  algebraic  formulae  into 
numbers  and  tabulated  and  reviewed  the  calculations  of 
the  third  group.  The  third  section  consisted  of  sixty  to 
eighty  persons,  who  simply  added  and  subtracted  the 
equations  given  them.  Their  labors  occupied  several 
years  and  the  results  were  bound  in  1  7  folio  volumes. 
In  these  tables  absolute  accuracy  is  essential,  and  that  is 
very,  very  rarely  attained.  In  a  set  of  logarithms  stereo¬ 
typed  by  Mr.  Babbage,  the  proof  was  compared  number 
by  number  with  other  tables  seven  times,  never-the-less, 
in  the  last  reading  thirty-two  errors  were  discovered. 


o 14313 


After  stereotyping  the  proof  was  compared  figure  by 
figure  four  times  and  eight  more  errors  discovered. 
Other  tables,  after  having  been  in  use  for  years,  have 
been  found  to  contain  hundreds  of  errors. 

Becoming  intensely  interested  in  these  tables  and  the 
methods  for  preparing  and  copying  them,  Mr.  Babbage, 
as  early  as  1819,  gave  careful  thought  to  the  invention 
of  a  machine  that  would  calculate  and  print  them  without 
the  intervention  of  human  hands  and,  therefore,  without 
error.  By  1822  he  had  made  a  small  machine  that 
would  calculate  simple  formulae,  such  as  multiplication 
tables  and  squares  up  to  eight  figures. 

In  a  letter  of  this  same  year  to  the  President  of  the 
Royal  Society,  he  not  only  describes  this  machine,  but 
adds  that  he  had  already  designed  a  method  for  printing 
faultlessly  the  results,  and  that  he  also  had  in  mind 
machines  to  multiply,  extract  roots,  and  various  other 
operations. 

The  machine  that  was  constructed  at  this  time  was 
very  simple,  consisting  of  but  few  parts,  but  these  were 
repeated  many  times.  On  trial,  it  was  found  possible  to 
calculate  from  30  to  40  numbers  a  minute,  which  was 
faster  than  a  man  could  copy  them  down.  He  claimed 
that  his  machine  only  needed  to  be  constructed  on  a 
larger  scale  to  calculate  any  and  all  tables  that  were 
characterized  by  regular  differences  between  succeeding 
terms,  and  to  add  printing  mechanism  that  would  produce 
and  record  absolutely  faultless  tables. 

He  called  this  first  machine  a  Difference  Engine, 
because  it  produced  successive  terms  of  a  table  auto¬ 
matically,  by  adding  the  requisite  differences  to  the 
last  term. 


To  illustrate  in  the  table  of  squares,  1-4-9-16-25, 
etc. 

By  subtraction  we  get  the  first  order  of  differences, 

3-5 -7-9,  etc. 

By  subtraction  again  we  get  the  second  order  of 
differences,  2-2-2,  etc. 

Now,  to  find  any  term,  we  have  only  to  add  the 
constant  2  to  the  last  known  difference  of  the  first  order 
to  the  last  known  square,  to  produce  the  following 
square : 

To  illustrate,  what  is  the  square  of  1  1  ?  The  square 
of  10=100,  the  square  of  9  =  81,  100 — 81  =  19 
2  + 19  + 100=  1 2 1,  the  square  of  1 1 .  This  is  compara¬ 
tively  a  simple  table.  There  are  tables  in  common  use 
that  have  five,  six,  and  even  seven  orders  of  differences, 
before  the  constant  is  found.  Mr.  Babbage,  in  1822, 
wrote  to  the  Prime  Minister  of  England  and  asked 
Government  assistance  in  constructing  a  Difference  En¬ 
gine  that  could  calculate  up  to  twenty  places  of  figures, 
and  that  would  also  print  automatically  the  results. 

The  Treasury  referred  the  request  to  the  Royal 
Society,  for  an  opinion  as  to  the  merits  of  the  invention. 
They  reported  promptly  that  it  was  “fully  adequate  to 
the  attainment  of  the  objects  proposed  by  the  inventor.” 
Soon  after,  in  1823,  the  sum  of  $7,500  was  appro¬ 
priated  to  this  end. 

Mr.  Babbage  at  once  set  to  work  to  construct  the 
enlarged  and  automatic  Difference  Engine.  Draftsmen 
were  set  to  work  making  the  drawings.  Mr.  Joseph 
Clement,  out  of  Maudsley’s  men,  was  given  charge  of 
the  mechanical  part,  and  for  four  years  the  work  pro¬ 
ceeded.  Tools  had  to  be  designed  and  constructed  to 


meet  the  demand  for  extreme  accuracy,  even  workmen 
-had  to  be  trained  to  a  nicety  of  execution  before 
unheard  of. 

In  1827  the  expense  incurred  had  amounted  to 
$I  7,000,  of  which  Mr.  Babbage  had  advanced  nearly 
$10,000.  At  this  time  his  health  was  poor  and  he  went 
to  Italy,  leaving  minute  instructions  to  be  followed  in 
building  the  machine  and  placed  $5,000  at  their  dis¬ 
posal.  Perceiving  that  the  probable  expense  would  be 
considerable,  he  asked  the  Government  for  another 
grant.  Lord  Wellington  inquired  of  the  Royal  Society 
for  an  investigation  as  to  whether  the  project  was  worth 
proceeding  with.  The  Society  gave  “their  decided 
opinion  in  the  affirmative.”  In  1829  the  Government 
made  another  grant  of  $7,500.  By  this  time  the 
expense  had  reached  $35,000.  Lord  Wellington  then 
personally  examined  the  machine,  and  the  Government 
made  a  grant  of  $7,500  more,  with  the  suggestion  that 
the  calculating  part  be  separated  from  the  printing  device. 

In  1830  still  another  grant  of  $15,000  was  made  by 
the  Government.  In  1832  the  Government  constructed 
a  fire  proof  workshop  near  Mr.  Babbage’s  residence  to 
contain  the  costly  drawings  and  machinery  which  had 
accumulated  dunng  the  years.  In  1833  a  portion  of  the 
machine  was  put  together,  which  completely  justified  the 
expectation.  It  could  calculate,  and  did  so  with  absolute 
accuracy,  tables  of  three  orders  of  differences  up  to  six¬ 
teen  figures. 

Meanwhile  difficulties  arose  between  Mr.  Babbage 
and  Mr.  Clement,  who  had  charge  of  the  construction. 
The  latter  had  an  increasing  sense  of  the  value  of  his 
part  of  the  work,  and  his  charges  grew  apace.  At 


length  Mr.  Babbage  secured  consent  to  have  Govern¬ 
ment  Engineers  examine  all  accounts  before  being  paid. 
There  being  some  delay  in  payments,  Mr.  Babbage  was 
accustomed  to  advance  money.  In  1834,  he  declined 
to  do  this  longer,  and  the  result  was  that  Mr.  Clement 
withdrew,  taking  with  him  many  of  the  best  workmen 
and  all  the  special  tools  that  he  had  designed  and  built, 
which  according  to  the  custom  of  the  day  he  had  a 
right  to  do,  even  though  the  Government  had  paid  for 
them.  Then  there  were  vexatious  delays,  as  to  whether 
the  Government  would  meet  Mr.  Clement’s  terms  or 
secure  some  one  else  for  the  construction. 

Meanwhile  an  entirely  new  idea  came  to  Mr.  Bab¬ 
bage  by  which  he  could  construct  a  calculating  machine 
of  far  greater  range  than  the  Difference  Engine. 
Mr.  Baggage  felt  that  it  was  not  right  to  ask  the 
Government  to  complete  the  first  machine  without  mak¬ 
ing  known  to  them  his  new  discovery.  Perhaps  also, 
and  it  would  be  quite  natural,  he  rather  hoped  that  the 
Government  would  abandon  the  old  and  start  at  once 
the  construction  of  the  new.  At  any  rate,  while  the 
question  was  being  discussed,  political  questions  became 
involved  and  the  matter  was  not  decided  until  1842, 
when  it  was  definitely  given  up.  The  part  of  the 
machine  that  was  completed  was  sent  to  the  Museum  of 
King’s  College,  London,  and  later  sent  to  South  Kensing¬ 
ton  and  the  uncompleted  parts  distributed  among  friends 
and  institutions,  as  souveniers. 

The  entire  cost  of  this  machine  to  the  Government, 
exclusive  of  the  fire  proof  building,  had  been  $80,000. 
Not  one  penny  came  to  Mr.  Babbage  as  a  recompense 
for  his  labors  of  twenty  years.  In  addition  to  what  the 


Government  had  expended  on  the  construction,  Mr. 
Babbage  had  also  expended  fully  as  much  more  and 
considerable  sums  for  personal  expenses,  experiments, 
travel,  and  research.  Although  this  machine  was  never 
completed,  it  has  been  thought  by  some  that  the  money 
had  been  well  expended,  because  of  the  habits  of  extreme 
accuracy  and  precision  that  were  introduced  into  English 
machine  construction,  by  the  many  workmen  and  drafts¬ 
men  who  received  their  training  under  Babbage  and 
Clement  and  then  passed  on  to  other  shops,  carrying 
with  them  the  skill  and  method  there  acquired. 

The  construction  of  machine  tools  was  certainly 
greatly  enriched  by  the  necessities  involved  in  the  con¬ 
struction  of  this  invention. 

From  1828  to  1839,  Mr.  Babbage  had  been  Lu¬ 
casian  Professor  of  Mathematics  at  Cambridge.  He  had 
made  several  journeys  to  the  Continent  and  written  many 
letters  and  essays.  One  book,  published  in  1834,  called 
“The  Economy  of  Machines  and  Manufactures,”  summed 
up  his  consideration  of  the  manufactures  of  the  time. 
This  book  was  widely  printed  and  read  for  several 
decades,  and  did  much  to  extend  the  modern  system  of 
manufacture  by  machinery. 

Once  only,  in  1832,  he  tried  to  enter  public  life,  but 
was  defeated. 

In  our  next  number  the  story  of  Mr.  Babbage  will 
be  continued  wdth  an  account  of  his  greatest  invention, 
the  Analytical  Engine,  which  was  the  most  complicated 
mechanism  ever  conceived  by  the  mind  of  man. 

Dwight  Goddard. 


Copyrighted,  1904, 
By  Wyman  &  Gordon. 


SHORT  STORIES  OF  ENGINEERS 


ARE  PUBLISHED  MONTHLY  IN  PLACE  OF  A 
======  CATALOGUE  ===== 


We  have  issued  the  following 

JAMES  WATT 

MATTHEW  BOULTON 
ROBERT  FULTON 

GEORGE  STEPHENSON 
JAMES  NASMYTH 

SIR  HENRY  BESSEMER 

SIR  WILLIAM  SIEMENS 

ALFRIED  KRUPP 
ELIAS  HOWE 

JOHN  ERICSSON 

SIR  JOSEPH  WHITWORTH 
THOMAS  NEWCOMEN 

BENJAMIN  FRANKLIN 

JOHN  FITCH 

OLIVER  EVANS 

JOHN  STEVENS 
ELI  WHITNEY 

THOMAS  BLANCHARD 
PETER  COOPER 

ALEXANDER  L.  HOLLEY 
JAMES  B.  EADS 

WILLIAM  R.  JONES 

RICHARD  ARKWRIGHT 
WILLIAM  MURDOCK 

RICHARD  TREVITHICK 
KRISTOFER  POLHEM 

WILLIAM  SYMINGTON 
HENRY  MAUDSLEY 

Others  to  follow. 


Many  of  these  are  out  of  print. 


WE  SEND  THESE  STORIES  TO  REMIND  YOU  THAT 

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HIGH  GRADE  DROP  FORGINGS 


WYMAN  &  GORDON 


CLEVELAND.  OHIO 
WORCESTER.  MASS. 

MANUFACTURERS  OF 


Drop  Forgings 


HIGH  GRADE  WORKMANSHIP 

We  employ  only  first  class  workmen  and 
up-to-date  machinery. 

HIGH  GRADE  MATERIAL 

We  order  on  analysis  and  have  our  own 
Chemical  Laboratory  to  know  what  we 
receive. 

HIGH  GRADE  TESTS 

We  have  acquaintance  with  methods  of 
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By  reason  of  our  T^o  Factories  located 
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r-J 


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A  SHORT  STORY  OF 

CHARL^  BABBAGE 

Part  II. 

The  Analytical  Engine 


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March,  1905 

WYMAN  &  GORDON 


Cleveland.  Ohio 


Worcester.  Mass. 


SHORT  STORIES  OF  ENGINEERS 

ARE  PUBLISHED  IN  PLACE  OF  A  CATALOGUE 


We  have  issued  the  following 

JAMES  WATT 

MATTHEW  BOULTON 
ROBERT  FULTON 

GEORGE  STEPHENSON 
JAMES  NASMYTH 

SIR  HENRY  BESSEMER 

SIR  WILLIAM  SIEMENS 

ALFRIED  KRUPP 
ELIAS  HOWE 

JOHN  ERICSSON 

SIR  JOSEPH  WHITWORTH 
THOMAS  NEWCOMEN 

BENJAMIN  FRANKLIN 

JOHN  FITCH 

OLIVER  EVANS 

JOHN  STEVENS 
ELI  WHITNEY 

THOMAS  BLANCHARD 
PETER  COOPER 

ALEXANDER  L.  HOLLEY 
JAMES  B.  EADS 

WILLIAM  R.  JONES 

RICHARD  ARKWRIGHT 
WILLIAM  MURDOCK 

RICHARD  TREVITHICK 
KRISTOFER  POLHEM 

WILLIAM  SYMINGTON 
HENRY  MAUDSLEY 
CHARLES  BABBAGE 
Others  to  follow. 


Many  of  these  are  out  of  print. 


HIGH  GRADE  DROP  FORGINGS 

MADE  ONLY  ON  ORDER 

WYMAN  (SI  GORDON 


o 


CHARLES  BABBAGE 


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Part  2 


THE  ANALYTICAL  CALCULATING 

MACHINE 

4jT  WAS  not  decided  by  the  Government  of  England 
^  to  discontinue  the  construction  of  the  Difference 
Machine  until  1842,  almost  ten  years  after  work  upon 
it  had  ceased.  Meanwhile  Mr.  Babbage  had  given 
much  thought  and  expense  in  perfecting  his  new  and 
vastly  more  complicated  calculating  machine. 

The  Difference  Engine  was  designed  to  calculate 
tables  by  simple  addition  of  the  proper  differences.  The 
Analytical  Engine  was  designed  to  work  out  the  alge¬ 
braic  development  of  any  formula  whose  law  was  known 
and  to  convert  it  into  numbers.  In  fact,  Mr.  Babbage 
declared  that  if  constructed  it  could  solve  any  algebraic 
problem  the  successive  steps  of  which  could  be  conceived 
of  by  the  human  mind,  do  it  automatically  and  print  the 
result  without  the  possibility  of  error. 

In  a  letter  Mr.  Babbage  thus  describes  it : 

It  IS  intended  to  include  1 00  numbers,  susceptible 
of  changing  each  may  consist  of  25  figures 
any  given  function  which  can  be  expressed  by  addition, 
subtraction,  multiplication,  division,  extraction  of  roots,  or 
the  elevation  of  powers,  the  machine  will  calculate  its 


numerical  value;  it  will  afterward  substitute  this  value  in 
place  of  V  or  any  other  variable  and  will  calculate  the 
second  function  with  respect  to  V;  it  will  reduce  to  tables 
almost  all  equations  of  finite  differences.” 

In  the  Difference  Engine  the  exact  method  for  adding 
was  immaterial  because  a  simplification  of  it  only  affected 
one  or  two  hundred  parts,  but  in  the  Analytical  Engine, 
the  mechanism  for  performing  the  elementary  operations 
of  adding,  subtraction,  dividing  and  multiplying  became 
so  important  that  any  change  affected  thousands  upon 
thousands  of  parts.  In  fact  the  machine  could  only  exist 
by  inventing  for  it  a  mechanical  method  of  addition  of  the 
utmost  simplicity.  It  is  said  that  Mr.  Babbage  and  his 
assistants  designed  and  partly  constructed  over  twenty 
different  methods  before  the  desired  simplicity  was 
attained. 

The  system  of  addition  finally  decided  upon  was  , 
extremely  simple  and  yet  it  not  only  added  all  digits  at 
once,  but  included  in  the  total  all  amounts  carried  and 
what  is  more  wonderful,  had  an  “anticipating  caniage,” 
that  included  in  the  total  all  the  amounts  carried  of  the 
carryings.  Thus  any  addition  could  be  performed  auto¬ 
matically  at  one  operation,  without  the  necessity  of  a  sub¬ 
sequent  operation  to  include  the  carryings. 

4- 

The  Engine  was  not  a  combination  of  machines,  the 
one  to  add,  another  to  subtract,  another  to  divide,  but 
was  designed  as  one  machine,  so  arranged  that  any 
operation,  or  any  combination  of  operations,  could  be 
performed  automatically  at  will.  It  consisted  in  the 
main  of  two  sets  of  columns,  the  one  called  the  Mill  and 
the  other  the  Store. 


The  Mill  consisted  of  a  series  of  columns  made  up  of 
discs,  into  which  was  placed  the  quantities  about  to  be 
operated.  The  Store  consisted  of  a  larger  number  of 
columns  into  which  all  the  variables  about  to  be  operated 
upon  were  placed,  and  into  which  all  those  quantities, 
which  had  arisen  by  result  of  other  operations  were 
placed. 

He  thus  separated  the  operations  from  the  objects 
acted  upon. 

“All  the  shifts  which  have  to  take  place,  such  as 
carrying,  borrowing,  etc. — changing  addition  into  sub¬ 
traction,  or  shifting  the  decimal  place,  are  affected  by  a 
system  of  rotating  cams,  acting  upon  or  actuated  by  bell 
cranks,  tangs,  clutches,  escapements.  These  clutches  and 
bell  cranks  control  the  process  effected,  or  being  them¬ 
selves  suitably  directed,  secure  that  the  proper  process 
should  be  performed  on  the  proper  subject  matter  and 
duly  recorded  or  used  as  required.” 

The  columns  that  make  up  the  Store  contained  a 
series  of  wheels  that  received  the  results  of  operations 
performed  by  the  Mill  and  served  as  a  store  of  numbers 
yet  to  be  used.  The  wheels  gear  into  a  series  of  racks, 
which  in  turn  are  operated  by  cards. 

These  cards  were  the  new  thought  that  came  to  Mr. 
Babbage  when  he  was  constructing  the  Difference 
Engine  and  which  brought  him  visions  of  the  possibilities 
of  the  new  machine  and  led  him  to  lose  interest  in  the  old. 

The  cards  themselves  were  no  new  invention.  They 
were  invented  by  Jacquard  to  control  the  introduction  of 
threads  in  weaving  brocade.  It  flashed  into  Mr. 
Babbage’s  mind  that  he  could  use  these  cards  to  indicate 


successive  operations  in  a  calculating  machine  that,  with 
this  equipment,  would  have  a  power  over  complicated 
arithmetical  operations  that  would  be  nearly  unbounded. 

These  cards  were  perforated  by  different  combina¬ 
tions  of  holes  and  were  then  linked  together  as  a  chain 
and  arranged  to  pass  successively  over  a  set  of  wires. 
The  wires,  corresponding  to  the  holes,  would  drop 
through  and  indicate  by  suitable  connections  the  desired 
operations  of  the  Mill. 

Having  the  machine,  all  that  human  brains  are  called 
upon  to  do  is  to  perforate  successive  cards  and  then 
operate  the  machine,  when  the  desired  operations  would 
follow  without  possibility  of  error. 

In  the  Analytical  Engine  there  were  two  principal 
sets  of  these  cards,  one  to  indicate  operations,  one  to 
indicate  the  columns  of  variables  upon  which  the  results 
are  to  be  presented. 

These  cards  thus  arrange  the  various  parts  of  the 
machine  and  then  execute  the  processes. 

ILLUSTRATION. 

(/)  mx  +  ny  =  d 
(2)  rn  X  +  ny  =  d' 
dn  —  d’n 

X  = - ^ - r- 

ran  —  m  n 

d'm  —  dm' 

y  = - r- 

mn  —  mn 

To  find  the  value  of  x  and  y  eleven  successive 
operations  must  be  performed,  as  indicated  in  the  follow¬ 
ing  tables : 


Columns 
on  which 
are  in¬ 
scribed  the 
primitive 
data. 


•Vn  =  m 


W.  = 


IV,  = 


'V,  = 


= 


m 


‘V,  =  d> 


c  Cards  of  the 
operations. 


1 

2 

3 

4 

5 

6 

7 

8 
9 
10 
11 


^  Ti 

•s? 

«-  c 
o)  o 

5  ‘- 
z  ^ 


2 


>> 


>» 


>» 


»> 


>» 


j= 
u  . 
?.  c 
o 


O  a 

a  i: 
3  S* 

s  ° 


X 

X 

X 

X 

X 

X 


Variable  cards. 


Columns  acted 
on  by  each 
operation. 


Vo  X  = 
Va  X  ‘Vi  = 
Vj  X  'V4  = 
V5  X  ‘V,  = 
Vo  X  ‘V,  = 
V2  X  'V3  = 


Ve  -  ‘V;  = 


V  —  IV 
'^8  ''9 


V  —  IV  — 

''10  '^11  — 


V,3^%2  = 


Vi.^‘V,, 


Columns 
that  receive 
the  result 
of  each 
operation. 


‘Ve  . 

‘V7  . 

%  . 

’Vo  . 

1 V 

''10 . 

*  V 

’V12 . 

'Vi3 . 

•Vh . 

•  V 

''15 . 

IV 

*  16 . 


Indication  of 
change  of  value 
on  any  column. 


{ 

{ 

{w:= 

{iv- 


’V3  = 
IV,  = 
1V2  = 

w.  = 


:} 
:} 
:} 
:} 
:} 

f-lV2  =  0V2  1 

rV3  =0V3  I 
J‘Vo=«Vo1 
i’V7  =  %; 

/  'Vs  =  ‘'Vs  1 
I'Vo  =  % ; 

;'Vio=‘'v,,'i 

l'Vn=‘'V„/ 


'V 

‘V 

»V 

IV 

ov 

'V, 

OV 

ov 

ov 

ov 


I  ’V,3=‘’V,3l 

l'V,2=‘V,2j 
rvH=‘'v,a 
I  '  Vjo—  ®Vj.2  J 


Statement  of.  results. 


=mn' 


IV7  =m'n 
‘V3  =dn' 


IV9  =d'n 


^\\Q  =  d'm 
lV„  =  t/7«' 


IV, 2  =  772  n'— 


i7i  n 


*  V 13  =  7i^  —  d'n 


=  d' m  —  d  m' 


'V.s  = 


d  n'  —  d'  n 


•V 


ni  n'  —  111  n 
d*  m  —  d  vd 


=  x 


m  il  — m  ' 71 


T=y 


8 


Cards  for  these  variables  must  be  arranged  and  cards 
for  the  eleven  operations  and  then  all  that  remained  was 
to  place  the  mechanism  in  motion.  It  is  thus  seen  that 
anything  in  the  way  of  calculating  that  the  human  mind 
IS  capable  of  precisely  defining,  this  machine  would  be 
capable  of  performing. 

Anyone  at  all  versed  in  designing  machinery  will 
recognize  the  difficulties  involved  in  keeping  a  clear  con¬ 
ception  of  the  individual  motions  of  this  maze,  of  “wheels 
within  wheels.”  In  order  that  he  might  have  a  clearer 
insight  into  the  various  motions,  Mr.  Babbage  invented  a 
system  of  mechanical  notation,  by  means  of  which  he 


could  chart  the  syncronous  motions  of  every  part  of  even 
the  most  complicated  mechanism.  The  motion  of  each 
part  was  represented  by  a  vertical  line,  whose  length  was 
divided  into  units  of  motion.  On  each  side  of  this  line 
were  various  symbols  for  direction,  nature  (intermittent 
or  regular),  source,  etc.  These  tables  of  notation  were 
carried  to  such  refinement  that  in  designing  it  was  always 
possible  by  laying  a  straight  edge  across  the  chart  to  see 
at  a  glance  the  exact  position  and  status  of  every  part  at 
that  instant. 

It  is  said  that  at  one  stage  it  was  desirable  to  shorten 
the  time  in  which  a  certain  operation  was  performed. 
The  constructor  had  a  model  of  the  part  before  him, 
while  Mr.  Babbage  resorted  to  his  tables.  The  opera¬ 
tion  required  the  time  of  twelve  revolutions.  After  pro¬ 
longed  study,  they  found  ways  to  reduce  the  time  to 
eight  revolutions,  then  the  Constructor  gave  it  up,  but 
shortly  after  Mr.  Babbage  discovered  new  combinations 
by  which  it  was  crowded  into  four  revolutions. 

For  twenty  years  Mr.  Babbage  continued  work  on 
this  invention  in  his  own  house  and  at  his  own  expense. 
He  continuously  employed  draftsmen  and  mechanics,  and 
took  much  time  in  explaining  his  designs  to  visiting 
experts,  mathematicians,  and  philosophers. 

It  was  no  dream  of  a  crank.  It  was  the  consummate 
result  of  the  life-long  thinking  of  the  greatest  genius  for 
this  sort  of  thing  that  the  world  has  ever  seen.  The 
designs  were  examined  by  the  wisest  philosophers  and 
the  foremost  engineers  of  his  day,  who  again  and  again 
gave  commendation  and  endorsement  to  the  worth  of 
his  plans. 


To  be  sure,  only  a  small  part  of  the  Mill  was  ever 
built,  just  sufficient  to  show  the  method  of  adding  and 
subtracting  and  the  anticipating  carriage.  Part  was 
made  in  gun  metal  mounted  on  steel,  but  the  greater 
part  of  a  kind  of  pewter  hardened  by  zinc  and  moulded 
by  pressure.  All  the  principles  were  either  drawn  or 
constructed  in  models. 

A  great  many  experiments  were  made  and  special 
tools  designed  for  making  with  sufficient  precision  the 
multitude  of  little  wheels,  which,  in  some  cases,  amounted 
to  50,000,  and  the  various  methods  of  construction  were 
determined  upon.  Over  400  drawings  were  made,  of 
which  some  thirty  were  group  plans,  some  of  which  were 
of  elaborate  complication.  There  are  five  volumes  of 
sketches,  and  400  to  500  folio  pages  comprising  a  com¬ 
plete  mechanical  notation. 

There  was  very  little  description  made  of  it.  The 
philosophers  were  more  interested  in  speculation  over  its 
mathematical  possibilities  and  Mr.  Babbage  was  too  busy 
designing  until  the  infirmities  of  old  age  prevented  him. 
He  once,  however,  spoke  of  1 ,000  columns  with  50 
wheels  each  in  the  Store  alone,  and,  besides,  many 
thousand  wheels  mounted  on  axles  in  columns  for  the 
Mill  and  a  vast  machinery  of  cams  and  cranks  for  the 
control. 

It  was  a  marvel  of  mechanical  ingenuity  and  resource, 
in  detail  good,  but,  on  the  whole  only  a  theoretical  pos¬ 
sibility.  Probably  no  man  but  Mr.  Babbage  himself 
ever  understood  its  working. 

M.  Menabrea,  an  Italian  Military  Engineer,  made  a 
profound  study  of  it  in  1842,  but  admits  in  his  careful 


description  that  the  time  at  his  disposal  was  gone  before 
he  had  begun  to  master  its  more  abstruse  possibilities. 

The  Analytical  Engine  was  invented  in  1  834,  and 
it  was  1 848  before  Mr.  Babbage  felt  that  he  had 
mastered  its  main  design.  In  1 852  he  consulted  the 
Government  to  see  if  they  would  construct  it,  and  in 
1854  he  abandoned  work  upon  it. 

He  had  doubtless  expended  over  $  I  00,000  of  his 
private  fortune  on  the  two  machines.  Those  who  were 
cognizant  of  the  state  of  machine  construction  during 
these  years  aver  that  the  money  expended  was  more  than 
repaid  in  the  advance  caused  in  the  art  of  constructing 
machines  of  precision.  No  small  credit  should  be  given 
to  Mr.  Babbage  for  this  exceedingly  practical  result  of 
his  painstaking  efforts. 

The  printed  works  of  Mr.  Babbage  comprise  over 
80  titles  nearly  all  of  which  are  essays  on  mathematical 
and  philosophical  subjects.  He  died  in  London  in  1871. 


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